We present an investigation of three chemically peculiar (CP) stars and one CP star candidate that exhibit photometric periods below 12 h. New spectroscopic observations have been acquired that confirm the peculiar nature of all objects. HD 77013 and HD 81076 are classical CP1 (Am) stars, HD 67983 is a marginal CP1 (Am:) star and HD 98000 is a CP2 (Ap) star. We have procured observations from the ASAS-3 and SuperWASP archives and obtained additional photometry in order to verify the results from the sky survey data. We have derived astrophysical parameters and investigated the positions of our target stars in the MBol versus log Teff diagram, from which information on evolutionary status has been derived. We present period analyses and discuss each object in detail. From the available data, we propose pulsational variability as the underlying mechanism for the variability in HD 67983, HD 77013 and HD 81076, which offer the opportunity to study the interaction of atomic diffusion and pulsation. HD 67983 and HD 77013 exhibit multiperiodic variability in the. Doradus frequency realm; HD 81076 is a d Scuti star. The CP2 star HD 98000 exhibits monoperiodic variability with a frequency of f approximate to 2.148 cycles d(-1) (P approximate to 0.466 d), which we interpret as the rotational period. If this assumption is correct, HD 98000 is the alpha(2) Canum Venaticorum variable with the shortest period hitherto observed and thus a very interesting object that might help to investigate the influence of rotational mixing on chemical peculiarities.